Tag: nonlinear dynamics

Seeking Rogue Wave Origins
Rogue waves — rare waves much larger than any surrounding waves — have long been a part of sailors’ tales, but their existence has only been confirmed relatively recently. The exact mechanisms behind them are still a matter of debate. Laboratory experiments with mechanically-produced waves have created miniature rogue waves, but we still lack real-world observations of their formation.
To that end, researchers sailed the Southern Ocean, known for its rough waves, during austral winter and observed the state of the wind and waves nearby using stereo cameras. They found that young wind-driven waves tend to be steeper, and they move slower than the wind, as they’re still drawing energy from it. Older waves, in contrast, were shorter, less steep, and less likely have white caps from breaking. Overall, they found that strong winds could more easily drive young waves into the nonlinear growth that leads to rogue waves. (Image credit: S. Baisch; research credit: A. Toffoli et al.; via APS Physics)
April 30, 2024
Testing Waves in High Gravity
Where waves crash and meet, turbulence is inevitable. But exactly how large waves interact — whether in the ocean, in plasma, or the atmosphere — is far from understood. A new experiment is teasing out a better physical understanding by tweaking a variable that’s been hard to change: gravity.
To do so, the researchers conduct their experiments in a large-diameter centrifuge (shown above) where they can create effective gravitational forces as high as 20 times Earth’s gravity. This increases the range of frequencies where gravity-dominated waves occur by an order of magnitude.
By studying this extended frequency range, the authors found something unexpected: the timescales of wave interactions did not depend on wave frequency, as predicted by theory. Instead, those interactions were dictated by the longest available wavelength in the system, a parameter set by the size of the container. It will be interesting to see if future work can confirm that result with even larger containers. (Image credit: ocean waves – M. Power, others – A. Cazaubiel et al.; research credit: A. Cazaubiel et al.; via APS Physics; submitted by Kam-Yung Soh)
January 9, 2020
Robotic Research Facilities
One of the major challenges in fluid dynamics is the size of the parameter spaces we have to explore. Because many problems in fluid dynamics are non-linear, making small changes in the initial set-up can result in large differences in the results. Consider, for example, a simple cylinder towed through a water tank. As the cylinder moves, vortices will form around it and shed off the back, causing the cylinder to vibrate. The details of what will happen will depend on variables like the cylinder’s size and flexibility, the speed it’s being towed at, and which directions it’s allowed to vibrate in. Mapping out the parameter space, even sparsely, could take a graduate student hundreds of experiments.
To speed up this process, engineers are now building robotic facilities like the Intelligent Towing Tank (ITT) shown above. Like graduate students, the ITT can work into the wee hours of the night, but, unlike graduate students, it never needs to eat, sleep, or stop experimenting. Now, one could use a facility like this to brute-force the answers by testing every possible combination of parameters, but even working 24 hours a day, that would take a long time. Instead, researchers use machine learning to guide the robotic facility into choosing test parameters in a way that optimizes the factors the researchers define as important.
Essentially, the system starts with experiments chosen at random within the parameter space, and then uses those results to select areas of interest until it’s gathered enough data to satisfy the limits specified by human researchers. In theory, a well-designed algorithm can dramatically reduce the number of experiments needed to explore a parameter space. (Image and research credit: D. Fan et al.; submitted by Kam-Yung Soh)
December 16, 2019
Modons
The spin of the Earth creates myriad eddies in our oceans, most of which move slowly westward at a speed dependent on their latitude. You can see many in the animation above as green and red rings slowly marching to the left. According to theory, it’s possible for two of these eddies to combine to become more than the sum of their parts; under the right conditions, the two conjoined eddies could become a modon, which, like a vortex ring, is capable of traveling far faster than its parental eddies. Despite the theory, however, no one had ever observed a modon in nature.
A new paper uses satellite imagery to identify nine modons in different locations around the world. One is shown above. Watch the eastern coast of Australia carefully, and you’ll see a modon form. It moves much faster than its surroundings, first southward toward Tasmania, then quickly eastward toward New Zealand. Thin black circles mark the two eddies that make up the modon. The strength and speed of these features makes them capable of pulling significant water mass with them. This suggests that they may play a role in ocean life, transporting water of different temperatures and nutrient content into regions it would not otherwise reach. (Image and research credit: C. Hughes and P. Miller; via Gizmodo)
March 2, 2018
Rogue Wave Recreated
If you look online, the term “rogue wave” gets thrown around a lot – a whole lot. And most of the videos you see of “rogue waves”, “freak waves”, and “monster waves” are just, in fact, big waves. What makes a deep-water ocean wave a rogue, scientifically speaking, is that it is extreme compared to its surroundings. One definition requires that a rogue wave be more than twice as tall as the height of average large waves in the area – like the rogue that takes out the Lego boat above. Outside the lab, this is a rare event – fortunately – because a true rogue wave has tremendous destructive power and seems to appear out of the blue.
This seemingly unpredictable behavior is thought to arise from nonlinear interactions between waves. Essentially, under the right conditions, a rogue wave grows monstrously large by sucking energy out of other surrounding waves. One way to try and predict rogue waves is to measure all the waves nearby and simulate their potential nonlinear interactions computationally – but this is time-consuming and requires a lot of computing power.
Instead, researchers have developed an alternative method, illustrated in the time series above. Instead of considering the rogue potential for all waves, they identify waves with characteristics that make them more likely to go rogue and focus on simulating those waves. In the animation, the wave packets are colored from green to red based on their increasing likelihood of turning into rogue waves. The algorithm is simple enough to run quickly on a laptop and can provide a couple minutes of warning to a ship’s crew – enough time to batten down before the wave hits. (Image credits: simulation – T. Sapsis et al., source; experiment: N. Ahkmediev et al., source; via The Economist and MIT News; submitted by 1307phaezr)
March 11, 2016
Printing in Glass
A group at MIT have created a new 3D printer that builds with molten glass. This allows them to manufacture items that would difficult, if not impossible, to create with traditional glassblowing or other modern techniques. One of the coolest aspects of this technique is that it can use viscous fluid instabilities like the fluid dynamical sewing machine to create different effects with the glass. You can see this around 1:56 in the video. Varying the height of the head and the speed at which it moves will cause the molten glass to fall and form into different but consistent coiling patterns. All in all, it’s a very cool application for using some nonlinear dynamics! (Video credit: MIT; via James H. and Gizmodo)
September 14, 2015
Water-Based Tractor Beam
Researchers in Australia have demonstrated a “tractor beam” capable of manipulating floating objects from a distance using surface waves on water. And, unlike some research, you can try to replicate this result right in the comfort of your own bathtub! When a wave generator oscillates up and down, it creates surface waves that move objects and particles on the water’s surface. When the wave amplitudes are small, the outgoing wave fronts tend to be planar, as in part (a) of the figure above. These planar waves push surface flow away from the wave generator in a central outward jet, and new fluid is entrained from the sides to replace it. This creates the kind of flowfield shown in the streaklines of part (b).
Increasing the amplitude of the surface waves drastically changes the surface flow’s behavior. Larger wave amplitudes are more susceptible to instabilities due to the nonlinear nature of the surface waves. This means that the planar wave fronts seen in part (a) break down into a three-dimensional wavefield, like the one shown in part (c). Near the wave-maker, the surface waves now behave chaotically. This pulsating motion ejects surface flow parallel to the wave-maker, which in turn draws fluid and any floating object toward the wave-maker. The corresponding surface flowfield is shown in part (d). The researchers are refining the process, but they hope the physics will one day be useful in applications oil spill clean-up. (Video credit: Australia National University; image and research credit: H. Punzmann et al. 1, 2; via phys.org; submitted by Tracy M)
August 22, 2014
4th Birthday: Rogue Waves
Rogue waves—individual, isolated waves far larger than the surrounding waves—were reported for centuries by sailors. But their stories of massive walls of water appearing in the open ocean were not corroborated until 1995 when a rogue wave struck an offshore platform. How these giant waves form is still under active research, but one leading theory is that nonlinear interactions between waves allow one wave to sap energy from surrounding waves and focus it into one much larger, short-lived wave. I first learned of rogue waves during a seminar in graduate school. At the time, this idea of nonlinear focusing had only been explored in simulation, but a few years later a research group was able to demonstrate the effect in a wave tank, as shown in the video above. Wait for the end, and you’ll notice how the rogue wave that takes down the ship is much larger than its predecessors. For more on rogue waves and their mind-boggling behavior, be sure to check my previous post on the subject. (Video credit: A. Chabchoub, N. Hoffmann, and N. Akhmediev)
July 23, 2014
The Fluid Dynamical Sewing Machine
Originally posted: 3 Jan 2012 Nonlinearity and chaos are important topics for many aspects of fluid dynamics but can be difficult to wrap one’s head around. But this video provides an awesome, direct example of one of the key concepts of nonlinear systems–namely, bifurcation. What you see is a thread of very viscous fluid, like honey, falling on a moving belt. Initially, the belt is moving quickly and the thread falls in a straight line. When the belt slows down, the thread begins to meander sinusoidally. With additional changes in the belt’s speed, the thread begins to coil. A multitude of other patterns are possible, too, just by varying the height of the thread and the speed of the belt. Each of these shifts in behavior is a bifurcation. Understanding how and why systems display these behaviors helps unravel the mysteries of chaos. (Video credit: S. Morris et al.)
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July 26, 2013
Liquid Mushrooms
The Rayleigh-Taylor instability can form at the interface between two liquids of different density under the influence of gravity, but a similar instability can occur in the absence of gravity. The image sequence above shows the Richtmyer-Meshkov instability, which occurs between two liquids of differing densities (regardless of their orientation) when impulsively accelerated. In this case, the experiment was conducted in a drop tower to simulate microgravity with the apparatus dropped on a spring to provide the impulse. As the instability grows, asymmetries appear. Nonlinear dynamics will amplify these distortions, eventually leading to turbulent breakdown. (Photo credit: C. Niederhaus/NASA Glenn, J. Jacobs/University of Arizona)
October 16, 2012